Hi Carrie! Welcome to the wonderful world of vintage machines!
Some questions for you. Does Beth sew as she is now? If so, there's no reason to tear her down to clean!! You can use pipe cleaners, qtips, cotton balls, along with sewing machine oil and get the machine cleaned up and pretty! A full tear down really isn't necessary, nor is it always the best option.
My suggestion would be to go to You Tube and do a search for MuvandFarve and watch some of Muv's videos for cleaning these old girls...